# Quantum Error Correction Circuit

## Contents |

Here we present **a quantum error** detection protocol on a two-by-two planar lattice of superconducting qubits. a, The phase-flip error correction protocol differs from the bit-flip protocol described in Fig. 3a only by single-qubit gates. Cross in:NPG journals • PubMed • Google ScholarSearch for M. Dark blue bars represent the ideal outcome for each ɛ and teal bars are measurements calibrated by the full X, Y and Z error rotation curves. weblink

Solid lines are simple cosine fits to the data. et al. Jost, E. The syndrome measurement "forces" the qubit to "decide" for a certain specific "Pauli error" to "have happened", and the syndrome tells us which, so that we can let the same Pauli

## Stabilizer Codes And Quantum Error Correction.

Rev. Log in now or Register for online access. A 86, 032324 (2012).CASArticle14.Chow, J. Phys.

Nature 382–385 **(2012).8.Bravyi, S.** & Kitaev, A. Rev. L. Quantum Error Correction Book Rev.

Reed1, L. Experimental realization[edit] There have been several experimental realizations of CSS-based codes. L.F., L.D.C. With that definition, a CNOT gate can be obtained with four single-qubit rotations plus a ECRij operation.

Overall, we find decent agreement between the experiment and ideal population outcomes (dark blue bars). Quantum Code 7 J. There are numerous ways of building the SC lattice with superconducting qubits and resonators. Figure 2: Pulse sequence and classical action of the three-qubit gate.

- et al.
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- Mod.
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- Errors of ɛ=Yθ, with θ∈[−π,π] are detected by both syndromes, as Y errors can be decomposed into a combination of bit- and phase-flip errors.
- Lett. 108, 070502 (2012).CASPubMedArticleDownload referencesAcknowledgementsWe thank M.
- Cory, M.
- Nature 504, 419–422 (2013).ISICASPubMedArticle20.Johnson, J.

## 5 Qubit Code

Although this renormalization provides an overall fairer comparison with the ideal case, it tends to increase the uncertainty in the bars, especially for the Z error due to the loss of Blakestad, J. Stabilizer Codes And Quantum Error Correction. State preservation by repetitive error detection in a superconducting quantum circuit. 5-qubit Quantum Error Correction Hence, for each of the 108 different measurement observables , has a single-shot variance that scales as .

A. http://vealcine.com/quantum-error/quantum-error-correction-usc.php A.W.C, J.M.G. If the three bit flip group (1,2,3), (4,5,6), and (7,8,9) are considered as three inputs, then the Shor code circuit can be reduced as a sign flip code. Semi-circular pieces reflect parity checks at the boundaries of the lattice. Steane Code

Inset shows ZX oscillations22 of the target qubit state population as a function of the cross-resonance drive length when the control qubit is in the ground (blue) or in the excited et al. Cambridge University Press. ^ W.Shor, Peter (1995). "Scheme for reducing decoherence in quantum computer memory". check over here First, the measured state fidelity (∼0.80–0.84) is higher than expected (∼0.75) from the measured fidelities of the five two-qubit gates and two independent single-shot measurements.

D. Bit Flip Memory Error F. Use of the American Physical Society websites and journals implies that the user has read and agrees to our Terms and Conditions and any applicable Subscription Agreement.

## The colormaps show the single-shot histograms of the syndrome measurements on Q2 and Q4.

However, it is possible to detect and correct errors without destroying coherence, by using quantum error correcting codes1. Conditioned on {0,+}, state tomography of the code qubits is performed, with a reconstructed final state (Pauli vector shown in Fig. 2a), commensurate with the originally prepared codeword state with a The X-syndrome qubit, Q4, is found in its excited state when a phase-flip error has occurred (c,d), whereas the Z-syndrome qubit, Q2, is found in its excited state as a result Fault-tolerant Quantum Computation et al.

et al. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/Article ToolsPDFDemonstration of a quantum error detection code using a square lattice of four superconducting qubitsDownload as PDFView interactive PDF in ReadCubeShare on This means that the Shor code can also repair sign flip error for a single qubit.[2] The Shor code also can correct for any arbitrary errors (both bit flip and sign http://vealcine.com/quantum-error/quantum-error-correction-ppt.php et al.

D. Res. The errors labelled as R and H correspond to a Yπ/2Xπ/2 operation, which maps the x–y–z axes in the Bloch sphere to y–z–x, and the Hadamard gate, respectively. Rev.

Rothwell and G. The three CNOTs that define the SWAP gate can be combined with the following ZZ parity check operation to simplify the circuit and three CNOT gates can be eliminated (b).